\(3^{x-1}+5.3^{x-1}=162\)

\(\Rightarrow3^{x-1}\left(5+1\right)=162\)

\(\Rightarrow3^{x-1}.6=162\)

\(\Rightarrow3^{x-1}=27\)

\(\Rightarrow3^{x-1}=3^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=4\)

\(3^{x-1}+5.3^{x-1}=162\Rightarrow3^{x-1}\left(1+5\right)=162\Rightarrow3^{x-1}.6=162\)

\(\Rightarrow3^{x-1}=162:6\Rightarrow3^{x-1}=27\Rightarrow x-1=3\Rightarrow x=4\)

`#3107`

b)

`2.3^x = 162`

`\Rightarrow 3^x = 162 \div 2`

`\Rightarrow 3^x = 81`

`\Rightarrow 3^x = 3^4`

`\Rightarrow x = 4`

Vậy, `x = 4`

c)

`(2x - 15)^5 = (2 - 15)^3`

\(\Rightarrow \)`(2x - 15)^5 - (2x - 15)^3 = 0`

\(\Rightarrow \)`(2x - 15)^3 . [ (2x - 15)^2 - 1] = 0`

\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=15\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x-15=1\\2x-15=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x=16\\2x=-14\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=-7\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)

`d)`

\(3^{x+2}-5.3^x=?\) Bạn ghi tiếp đề nhé!

`e)`

\(7\cdot4^{x-1}+4^{x-1}=23?\)

\(4^{x-1}\cdot\left(7+1\right)=23\\ \Rightarrow4^{x-1}\cdot8=23\\ \Rightarrow4^{x-1}=\dfrac{23}{8}\)

Bạn xem lại đề!

`f)`

\(2\cdot2^{2x}+4^3\cdot4^x=1056\)

\(\Rightarrow2\cdot2^{2x}+\left(2^2\right)^3\cdot\left(2^2\right)^x=1056\\ \Rightarrow2\cdot2^{2x}+2^6\cdot2^{2x}=1056\\ \Rightarrow2^{2x}\cdot\left(2+2^6\right)=1056\\ \Rightarrow2^{2x}\cdot66=1056\\ \Rightarrow2^{2x}=1056\div66\\ \Rightarrow2^{2x}=16\\ \Rightarrow2^{2x}=2^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)

Vậy, `x = 2`

_____

\(10 -{[(x \div 3+17) \div 10+3.2^4] \div 10}=5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)

\(\Rightarrow\left(x\div3+17\right)\div10+48=50\)

\(\Rightarrow\left(x\div3+17\right)\div10=2\)

\(\Rightarrow x\div3+17=20\)

\(\Rightarrow x\div3=3\\ \Rightarrow x=9\)

Vậy, `x = 9.`

=0 nhe

3^x-1+5.3^x-1=162

3^x-1.(1+5)=162

3^x-1.6=162

3^x-1=162:6

3^x-1=27

3^x-1=3^3

x-1=3

x=3+1

x=4

3^x(3+5.3)=162

3^x=9

x=2

3^x-1 +5.3^x-1=162

6. 3^x-1=162

3^x-1=27

x-1=3

x=4

\(3^{x-1}\)+5.\(3^{x-1}\)=162

\(\Leftrightarrow\)\(3^{x-1}\)(1+5)=162

\(\Leftrightarrow\)\(3^{x-1}\)=27

\(\Leftrightarrow\)\(3^{x-1}\)=3³

^{\(\Leftrightarrow\)}x-1=3

\(\Leftrightarrow\)x=4

Vậy x=4

Ta có : 3^{x - 1} + 5 . 3^{x - 1} = 162

 \(\Leftrightarrow\)3^{x - 1} . ( 1 + 5 ) = 162

\(\Leftrightarrow\)3^{x - 1} . 6 = 162

\(\Leftrightarrow\)3^{x - 1}  = 162 ÷ 6 = 27

\(\Leftrightarrow\)3^{x - 1} = 3³

\(\Leftrightarrow\)x - 1 = 3

\(\Leftrightarrow\)x = 4

Vậy : x = 4

Mình ko viết lại đầu bài nhé!

=> 3^x-1. (1+5) = 162

=>3^ x-1 . 6 = 162

=>3^x-1       =27

=>3^x-1        = 3^3

=>x-1          =3

=>x             = 4

Vậy x=4

3^x-1.(1+5)=162

=>3^x-1=162:6

=>3^x-1=27=3^3

=>x-1=3

=>x=4

vậy x=4 nhé!

bài này dễ woa

bài này để qua kết quả bảng 4 chứ mấy nữa

3^x-1+5.3^x-1=162

3^x-1 .(5 + 1)=162

3^x-1 . 6 =162

3^x-1  =162:6

3^x-1 =27

3^x-1  =3\(^3\)

x - 1 = 3

x       =  3 + 1

x      = 4

3^x-1+5.3^x-1=162

3^x-1.1+5.3^x-1=162

3^x-1.(1+5)=162.Suy ra:3^x-1=162:6=27

3^x:3=27.Suy ra:3^x=3.27=81=3⁴(81=3⁴)

Vậy x=4

CHÚC BẠN HỌC TỐT

\(3^{x-1}+5\cdot3^{x-1}=162\)    

\(3^{x-1}\cdot1+5\cdot3^{x-1}=162\) 

\(3^{x-1}\cdot\left(1+5\right)=162\)  

\(3^{x-1}\cdot6=162\)  

\(3^{x-1}=162:6\)  

\(3^{x-1}=27\)

\(3^{x-1}=3^3\) 

=> x-1=3

x=1+3

x=4

k co ah nha

3^x-1 + 5.3^x-1 = 162

 3^x-1. (1+5) = 162

3^x-1       =27

3^x-1        = 3^3

x-1          =3

x             = 4

Vậy x=4

\(3^{x-1}+5.3^{x-1}=162\)

\(\Rightarrow3^{x-1}.\left(1+5\right)=162\)

\(\Rightarrow3^{x-1}.6=162\)

\(\Rightarrow3^{x-1}=162:6=27=3^3\)

\(\Rightarrow x-1=3\)

\(\Rightarrow x=3+1=4\)